相关论文: Adjoint and Its roles in Sciences, Engineering, an…
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…
The resources compiled in this document provide an approach to embed and teach Ethics in Mathematics at the undergraduate level. We provide mathematical exercises and homework problems that teach students ethical awareness and transferable…
By the biadjoint triangle theorem, given a pseudomonad $\mathcal{T} $ on a $2$-category $\mathfrak{B} $, if a right biadjoint $\mathfrak{A}\to\mathfrak{B} $ has a lifting to the pseudoalgebras…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
We extend the operations of shorting and parallel addition from the cone of bounded nonnegative selfadjoint operators in a Hilbert space to the set of all nonnegative selfadjoint linear relations. New properties of these operations and…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct…
In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…
Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general…
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced…
We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an…
For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…